Synthetic Spectral Library of Optically Thick Atmospheres for Little Red Dots

Abstract

Little Red Dots (LRDs) challenge conventional models of active galactic nuclei. At rest-optical-to-near-infrared (IR) wavelengths, these compact extragalactic objects show blackbody-like continuum emission and spectral features reminiscent of stars, motivating models with an optically thick atmosphere at $T_{\rm\!\,eff}\sim4000-5000{\rm~K}$. We develop (and publicly release) a synthetic spectral library of optically thick atmospheres with gas conditions tailored for LRDs, parameterized by effective temperature $T_{\rm\!\,eff}$ and surface gravity $g$. Given the uncertain dynamical structure of LRDs, we interpret $g$ most directly as a photospheric density $ρ_{\rm\!\,ph}$. We show that blackbodies are only crude approximations to the emission from LRD-like atmospheres. Spectral features are abundant, many of which are sensitive diagnostics of photospheric density, including the overall curvature of the spectral energy distribution, the rest-$1.6{\rm~μm}$ spectral ''kink'' from $\rm H^-$ opacity, and the Ca II triplet (CaT) absorption at rest-8500 $\unicode{x212B}$. When compared against a local LRD, \egg, all three features consistently indicate a low photospheric density of $ρ_{\rm\!\,ph}\sim 10^{-11}{\rm~g~cm^{-3}}$ ($g\sim10^{-3}{\rm~cm~s^{-2}}$ in our library). This disfavors hydrostatic configurations and suggests a mass within the photosphere (black hole plus gas) of $10^4~M_\odot$, with an Eddington ratio $λ_{\rm Edd}\gtrsim20$, if the CaT width traces turbulent support at the photosphere in spherical symmetry; the inferred mass could be higher depending on the geometry and the radius probed by CaT. For higher redshift LRDs, we advocate for rest-near-IR spectroscopic surveys and high-resolution spectra of potential absorption lines as a test of the optically thick atmosphere scenario and as a unique probe of the central engine mass.

Figures (16)

• Figure 1: Grid of model parameters covered in this work. Points with multiple metallicity coverage are slightly shifted for visual clarity. The vertical plotting scale is different below $4000{\rm~K}$, where coverage is sparser. Only models with $\xi_{\rm mtb}=2{\rm~km~s^{-1}}$ are shown, but we also calculated hydrostatic models with $\xi_{\rm mtb}=10{\rm~km~s^{-1}}$, $4000{\rm~K}\leq T_{\rm eff}\leq5000{\rm~K}$, and $\rm[M/H]=-1$. For the meaning of "hydrostatic" (filled markers) versus "no-$g_{\rm rad}$" (empty markers) models, see Section \ref{['subsec:super-Eddington_scenarios']}.
• Figure 2: Photosphere gas density $\rho_{\rm ph}$ as a function of gravity. Multiple metallicities are shown only for $T_{\rm eff}=4000{\rm~K}$ for visual clarity. Only models with $\xi_{\rm mtb}=2{\rm~km~s^{-1}}$ are shown; results are similar for $\xi_{\rm mtb}=10{\rm~km~s^{-1}}$. For the meaning of "hydrostatic" (filled markers) versus "no-$g_{\rm rad}$" (empty markers) models, see Section \ref{['subsec:super-Eddington_scenarios']}. For a given $T_{\rm eff}$ and $\rm [M/H]$, $\rho_{\rm ph}$ increases with $\log g$.
• Figure 3: Overview of synthetic spectra and the spectral features to be discussed. Two models at $T_{\rm eff}=5000{\rm~K}$ broadly agree with the spectrum of UNCOVER-45924 Labbe2024, but their different $\log g$ values give different Balmer break and Ca HK absorption strengths. Two models at $T_{\rm eff}=5000{\rm~K}$ broadly agree with the spectrum of J1025-1402 Lin2025b, but the low-gravity one gives a narrower optical-to-near-IR SED, stronger Ca2 triplet (CaT) absorption, and does not show a continuum turnover at $\lambda_{\rm rest}\sim1.6{\rm~\mu m}$ (the "$\rm H^-$ kink"). The low-gravity model is preferred for the Egg if we account for the additional galaxy and dust emission (Section \ref{['sec:application']}). All four models have $\rm[M/H]=-1$ and $\xi_{\rm mtb}=2{\rm~km~s^{-1}}$. The wavelength ranges of our synthetic photometry bands to be used later, from $\tilde{\rm B}$ to $\tilde{\rm K}$, are shaded in color.
• Figure 4: Color-color diagram of synthetic spectra (left: $\xi_{\rm mtb}=2{\rm~km~s^{-1}}$; right: $\xi_{\rm mtb}=10{\rm~km~s^{-1}}$) and observed LRDs. $\rm \tilde{B}-\tilde{R}_1$ and $\rm \tilde{R}_2-\tilde{Z}$ (see Figure \ref{['fig:overview']} and text for band definitions) capture the optical and near-IR slopes. Axes on the top and right give the color temperatures. Points below the dash-dotted "blackbody" line of $T_{\rm \tilde{B}-\tilde{R}_1}=T_{\rm \tilde{R}_2-\tilde{Z}}$ have SEDs narrower than a blackbody, i.e., with relatively red optical colors but blue near-IR colors. Gray vector indicates the change of colors by an SMC dust extinction of $A_V=1$. Model points are color-coded by $\log g$; those with the same $T_{\rm eff}$ and [M/H] are connected by gray lines. Three metallicity values are shown for $T_{\rm eff}=4000{\rm~K}$ and $\xi_{\rm mtb}=2{\rm~km~s^{-1}}$, while only $\rm[M/H]=-1$ is shown for other cases. Empty markers indicate no-$g_{\rm rad}$ models. The JWST LRD samples in deGraaff2025b and the EggLin2025b are shown in comparison; for the Egg, the "total" point measures the original spectrum and the "atmos." point measures the spectrum subtracted by a best-fit young galaxy model (Section \ref{['sec:application']}). For cool models with $T_{\rm eff}<5000{\rm~K}$, low-$\log g$ atmospheres may give SEDs significantly narrower than a blackbody.
• Figure 5: Similar to Figure \ref{['fig:color_color']}, but for longer wavelengths, i.e., $\rm \tilde{R}_1-\tilde{Z}$ vs. $\rm \tilde{J}-\tilde{H}$. Three metallicity values are shown for $T_{\rm eff}=4000,5000{\rm~K}$ and $\xi_{\rm mtb}=2{\rm~km~s^{-1}}$, while only $\rm[M/H]=-1$ is shown for other cases. Microturbulence $\xi_{\rm mtb}=10{\rm~km~s^{-1}}$ is shown as thin solid lines for $T_{\rm eff}=4000, 4500, 5000{\rm~K}$ and $\rm[M/H]=-1$ but without markers for visual clarity. The JWST LRD samples in deGraaff2025b and the EggLin2025b are shown in comparison; for the Egg, the "total" point measures the original spectrum and the "atmos." point measures the spectrum subtracted by a best-fit young galaxy model dominating in the UV and a warm dust emission model dominating in the mid-IR (Section \ref{['sec:application']}). Model colors at long wavelengths strongly depend on $\log g$ and are insensitive to $\xi_{\rm mtb}$; the models suggest at least $\log g<-2$ for the Egg.